How to find Pearsonian's Coefficient of Kurtosis (γ₂) for a distribution?

Question:

Find Pearsonian's Coefficient of Kurtosis (γ₂) for a distribution when μ₂ = 16 and μ₄ = 1024.


Solution:

Step 1: Find β

β₂ = μ₄ / μ₂²

β₂ = 1024 / 16²

β₂ = 1024 / 256

β₂ = 4


Step 2: Find Pearsonian's Coefficient of Kurtosis (γ₂)

γ₂ = β₂ - 3

∴ γ₂ = 4 - 3

∴ γ₂ = 1

γ₂ > 0, we can say that the distribution is leptokutic.


Answer:

Pearsonian's Coefficient of Kurtosis (γ₂) is 1 for a distribution when μ₂ = 16 and μ₄ = 1024.


Video Solution:



How to find Pearsonian's Coefficient of Kurtosis (γ₂) for a distribution?